Solve {l}{x+1/y-1=2}{3/2-3/y-1=1}

$$\left. \begin{array} { l } { x + \frac { 1 } { y - 1 } = 2 } \\ { \frac { 3 } { 2 } - \frac { 3 } { y - 1 } = 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{11}{6} = 1\frac{5}{6} \approx 1.833333333$$

$$y=7$$

Solution Steps

Consider the second equation. Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(y-1\right), the least common multiple of 2,y-1.

$$2\left(y-1\right)\times \frac{3}{2}-2\times 3=2\left(y-1\right)$$

Use the distributive property to multiply 2 by y-1.

$$\left(2y-2\right)\times \frac{3}{2}-2\times 3=2\left(y-1\right)$$

Use the distributive property to multiply 2y-2 by \frac{3}{2}.

$$3y-3-2\times 3=2\left(y-1\right)$$

Multiply -2 and 3 to get -6.

$$3y-3-6=2\left(y-1\right)$$

Subtract 6 from -3 to get -9.

$$3y-9=2\left(y-1\right)$$

Use the distributive property to multiply 2 by y-1.

$$3y-9=2y-2$$

Subtract 2y from both sides.

$$3y-9-2y=-2$$

Combine 3y and -2y to get y.

$$y-9=-2$$

Add 9 to both sides.

$$y=-2+9$$

Add -2 and 9 to get 7.

$$y=7$$

Consider the first equation. Insert the known values of variables into the equation.

$$x+\frac{1}{7-1}=2$$

Subtract 1 from 7 to get 6.

$$x+\frac{1}{6}=2$$

Subtract \frac{1}{6} from both sides.

$$x=2-\frac{1}{6}$$

Subtract \frac{1}{6} from 2 to get \frac{11}{6}.

$$x=\frac{11}{6}$$

The system is now solved.

$$x=\frac{11}{6} y=7$$